How to find x(x-2)<0

Question

asked Dec 6, 2022 103k views

2 Answers

Jlmmns · Answer 1 · 2022-12-12T02:07:42+0000

Answer:

0<x<2

Explanation:

Hi there!

x(x-2)<0

Set x(x-2) equal to 0:

x(x-2)=0

Solve for x by using the zero product property:

x(x-2)=0

x=0 and
x=2

Now, we know that for the inequality
x(x-2)<0 , one of the following must be true:

1)
0<x<2

2)
x<0 or
x>2

To find out which one it is, 1) or 2), we can substitute a value into
x(x-2)<0 to see if the inequality is true.

For example, 1 takes place in between 0 and 2. If 1 satisfies
x(x-2)<0 , then
0<x<2 must be true. If it does not, then
x<0 or
x>2 must be true:

$1(1-2)<0\\1(-1)<0\\-1<0$

This inequality is true. Thus,
0<x<2 .

I hope this helps!